Direct measurement of the ³He⁺ magnetic moments

Helium-3 has nowadays become one of the most important candidates for studies in fundamental physics^1-3, nuclear and atomic structure^4,5, magnetometry and metrology⁶, as well as chemistry and medicine^7,8. In particular, ³He nuclear magnetic resonance (NMR) probes have been proposed as a new standard for absolute magnetometry^6,9. This requires a high-accuracy value for the ³He nuclear magnetic moment, which, however, has so far been determined only indirectly and with a relative precision of 12 parts per billon^10,11. Here we investigate the ³He⁺ ground-state hyperfine structure in a Penning trap to directly measure the nuclear g-factor of ³He⁺ [Formula: see text], the zero-field hyperfine splitting [Formula: see text] Hz and the bound electron g-factor [Formula: see text]. The latter is consistent with our theoretical value [Formula: see text] based on parameters and fundamental constants from ref. ¹². Our measured value for the ³He⁺ nuclear g-factor enables determination of the g-factor of the bare nucleus [Formula: see text] via our accurate calculation of the diamagnetic shielding constant¹³ [Formula: see text]. This constitutes a direct calibration for ³He NMR probes and an improvement of the precision by one order of magnitude compared to previous indirect results. The measured zero-field hyperfine splitting improves the precision by two orders of magnitude compared to the previous most precise value¹⁴ and enables us to determine the Zemach radius¹⁵ to [Formula: see text] fm.